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 (${BVI}_C$) and the 2MASS (${JHK}_s$) 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 $T_{eff}\sim 3600K$, 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 ($T_{eff}\lesssim 5500K$) and metal-rich ($\left[Fe/H\right]=+0.37$) 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 ($T_{eff}\lesssim 4800K$), 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 $E(B-V)=0.105\pm 0.014$, [M/H]$=+0.42\pm 0.07$, ${(m-M)}_0=13.04\pm 0.08$, and the age of 9.5 ± 0.3 Gyr for NGC 6791.